Abstract: The synchronization and stabilization issues are investigated for a large-scale system, which is composed of N identical Lorenz systems and they are coupled together with the first state variable of each subsystem. When uncontrolled, the sufficient condition of synchronization for such the large-scale system is derived by choosing an adaptive feedback gain equation. And if choosing an appropriate controller, the large-scale system can be stabilized. Such a controller is composed of two components, i.e., the state feedback controller is simple and easy to implement, and the other one relates to coupling coefficient. As a result, the final expression is in the terms of the Linear Matrix Inequalities (LMIs). A simulation example is provided to illustrate the design procedure of the proposed method and its feasibility and effectiveness.